In the art of building “mystery clocks”, drive mechanisms may or may not be visible. However, in “mystery clocks” the driving mechanisms are intentionally designed to impede the unwary observer when trying to understand how the drive actually functions.
A few clocks with two independent balanced hands have been built in the past. Some of the basic principles utilized in the design and operation of balanced hand clocks are described in an article entitled “The Balanced-Independent-Hand Clock”, by Rubens A. Sigelmann, The National Association of Watch and Clock Collectors, Inc. (“NAWCC”) Bulletin, Vol. 44/2, pages 177-182, April, 2002. The basic principles as previously known in the art are illustrated in FIGS. 1 and 2. One type of a balanced-hand for a clock can be represented by the simplified illustration provided in FIG. 1. The balanced hand 10 is represented as extending between (a) a center of mass m1 located for reference purposes as at the pointing end 12 of indicating arrow 14, and (b) a center of mass m2 situated for reference purposes at location identified by reference numeral 16. The balanced hand 10 is suspended from, and rotates freely around, a pivot axis 18. The mass m1 represents all the mass above the point of suspension or pivot axis 18. Distance I1 represents the distance between the center of mass for mass m1 and the point of suspension at pivot axis 18. Similarly, m2 represents all mass, except for mass m3 discussed below, below the point of suspension and pivot axis 18. Distance I2 represents the distance between the center of mass for mass m2 and the point of suspension at pivot axis 18. Also as indicated in FIG. 1, the mass m3 rotates along a circle 20 of radius r.
Referring now to FIG. 1, consider the case when mass m3 rotates by an angle beta (β) in the counterclockwise direction. Due to the force of gravity GR as indicated downward along reference line 22, the new position of the balanced hand 10 is given by the angle alpha (α) from the vertical reference line 22. A balanced hand exhibits no eccentricity if, when the angle beta (β) is equal to zero (0), the balanced hand aligns along the gravity direction of reference line 22, as shown in FIG. 1. Thus, for a balanced hand without eccentricity the angles alpha (α) and beta (β) are related by the equation [1]:m1l1 sin(α)=(m2+m3)l2 sin(α)+m3r sin(α−β)
Thus, as described by the equation [1], in the event that the mass and distance balance relationships of the balanced hand is described by the equation [2] belowm1l1=(m2+m3)l2then the only way the equation may be satisfied is if the angle alpha (α) equals the angle beta (β). This is the condition for the balanced hand being balanced. Consequently, in a precisely balanced hand, when the mass m3 rotates a prescribed angle beta (β) in the counterclockwise direction about the movement axis at 16 of movement 17, the balanced hand rotates exactly the equivalent angle alpha (α) in the clockwise direction about the pivot axis 18.
Prior art clocks as described in the article noted above utilize two independent balanced hands, namely, one for the minute hand and one for the hour hand. In those clocks, a quartz movement drives a mass m3 in each of the balanced hands. However, in such prior art clocks, the minute balanced hand mass m3 (minute) is attached to the axle 16 of the movement in the minute hand 10, and a the hour balanced hand mass m3 (hour) is attached to an axle of the movement in an hour hand, with construction similar to that shown for the minute hand depicted in the prior art minute hand design depicted in FIGS. 1 and 2.